Structure fundamental vibrational frequencies

One type of single point calculation, that of calculating vibrational properties, is distinguished as a vibrations calculation in HyperChem. A vibrations calculation predicts fundamental vibrational frequencies, infrared absorption intensities, and normal modes for a geometry optimized molecular structure. 

Thus the x-ray data do not decide between this structure and a truly plane structure. Evidence from another source is at hand, however. A plane C03= or N03 ion should show three characteristic fundamental vibrational frequencies. These have been observed as reflection maxima in the infra-red region. But two of the maxima, at 7 m and 14m, are double,27 and this doubling, which is not explicable with a plane configuration, is just that required by a pyramidal structure, the separation of the components giving the frequency of inversion of the pyramid.28... 

The photoelectron spectra of the isoelectronic molecules N2 and CO have peaks corresponding to the ionization energies, 7, given in Table 4.3. The peaks corresponding to the ionized molecules have vibrational structure, with vibrational separations in wavenumbers given in Table 4.3. The fundamental vibration frequencies of the neutral molecules N2 and CO are 2345 and 2143 cm1, respectively. 

The adopted "V" shape molecular structure with nine fundamental vibrational frequencies was obtained from an estimation by Mann (3). The bond distance Be-0 and Be-F were estimated to be the same as those in BeO(g) and BePg(g), respectively. The... 

The structure and vibrational frequencies are those calculated from an ionic model by Berkowitz (9). The sixth fundamental was arbitrarily lowered from 206 to 100 cm" since the resulting entropy increase (1.4 cal K" mol" at 1300 K.) improved the... 

The four fundamental vibrational frequencies and the Si-H bond distance are the result of gas-phase infrared and Raman spectral studies by Kattenberg and Oskam (8). They are in excellent agreement with values selected from earlier work as given in the compilations of Janz and Mikawa (9) and Shiraanouchi (1 ). The heat capacity and entropy calculations are based on a tetrahedral structure. The S°(298.15 K) = 48.89 0.01 cal K mol is in good agreement with another evaluation ( ). 

EVA descriptors were recently proposed by Ferguson et al. [Ferguson et al, 1997 Turner et al., 1997] as a new approach to extract chemical structural information from mid- and near-infrared spectra. The approach is to use, as a multivariate descriptor, the vibrational frequencies of a molecule, a fundamental molecular property characterized reliably and easily from the potential energy function. The EigenVAIue (EVA) descriptor is a function of the eigenvalues obtained from the normal coordinate matrix they correspond to the fundamental vibrational frequencies of the molecule, which can be calculated using standard quantum or molecular mechanical methods from -> computational chemistry. 

Figure 1 shows the structure of all-trans-polymethineimine and Table 1 lists the optimized geometries for both HF and MBPT(2) methods with three basis sets, STO-3G, 6-31G, and 6-31G [68], We can see that both the size of the basis sets and electron correlation have a strong influence on the stable structure, especially on the difference between the two bond lengths, Tn=c and Yc-n-Table 2 presents the HF and MBPT (2) fundamental vibrational frequencies for all-trans-polymethineimine [68], The vibrational frequencies listed in each... 

The vibrational spectra of all of the known actinide element hexafluorides can be interpreted on the basis of the structure of a regular octahedron. Malm et al. (56) have measured the infrared spectra of NpF and PuFe and have deduced the fundamental vibration frequencies (Table VI). 

Difluoroethyne is a short-lived molecule at room temperature and decomposes to yield a polymer and other reactive species. Its ground state geometric structure and vibrational spectrum have recently been investigated The best combined experimental and theoretical estimate of the equilibrium bond lengths gives 1.19 A for C—C and 1.28-1.29 AforC—F in a linear conformation, to be compared with the calculated numbers in Table 50. The measured fundamental vibrational frequencies are listed in Table 51 and are very... 

In view of the difficulty in obtaining spectral data for selectively isotopically substituted species, calculations of ground state rotational constants, centrifugal distortion constants, and fundamental vibration frequencies for species of the type B2H6 D have been performed. The calculations were based on existing zero-point average structural parameters. The enharmonic fundamental frequencies for all deuterated diboranes(6) are given [10]. 

Lunelli and collaborators described the crystal structure of sodium tmns-bis(dicyanomethylene)squarate 26 as well as computer calculations of the fundamental vibrational frequencies of the respective dianion [82]. In this study, the crystal structure of the free anion of sodium tra s-bis(dicyanomethylene)squarate 26 tetrahydrated reveals its Z)2h symmetry with an essentially planar structure (deviation of approximately 0.05 A). Water molecules were found to be essential in the crystal architecture because they coordinate with the sodium cations and provide stability to the crystal through strong hydrogen bonds. After determining the bond distances, the study concluded that the structure exhibits the lowest perturbation, as evidenced by the canonical forms with negative charge at the most electronegative atoms of the molecule. 

The linear structure of 93 was derived from experiments with labeled precursor molecules and by correlation of vibrational frequencies calculated from estimated force constants with the recorded IR absorptions. The three fundamentals were observed as well as the UV/VIS spectrum,131 which was resolved and analyzed by gas phase measurements.132 The predicted triplet ground state was confirmed by recording the ESR spectrum of 93 isolated in various matrices.131... 

Vibrational spectroscopy can help us escape from this predicament due to the exquisite sensitivity of vibrational frequencies, particularly of the OH stretch, to local molecular environments. Thus, very roughly, one can think of the infrared or Raman spectrum of liquid water as reflecting the distribution of vibrational frequencies sampled by the ensemble of molecules, which reflects the distribution of local molecular environments. This picture is oversimplified, in part as a result of the phenomenon of motional narrowing The vibrational frequencies fluctuate in time (as local molecular environments rearrange), which causes the line shape to be narrower than the distribution of frequencies [3]. Thus in principle, in addition to information about liquid structure, one can obtain information about molecular dynamics from vibrational line shapes. In practice, however, it is often hard to extract this information. Recent and important advances in ultrafast vibrational spectroscopy provide much more useful methods for probing dynamic frequency fluctuations, a process often referred to as spectral diffusion. Ultrafast vibrational spectroscopy of water has also been used to probe molecular rotation and vibrational energy relaxation. The latter process, while fundamental and important, will not be discussed in this chapter, but instead will be covered in a separate review [4],... 

The theory developed for perfect gases could be extended to solids, if the partition functions of crystals could be expressed in terms of a set of vibrational frequencies that correspond to its various fundamental modes of vibration (O Neil 1986). By estimating thermodynamic properties from elastic, structural, and spectroscopic data, Kieffer (1982) and subsequently Clayton and Kieffer (1991) calculated oxygen isotope partition function ratios and from these calculations derived a set of fractionation factors for silicate minerals. The calculations have no inherent temperature limitations and can be applied to any phase for which adequate spectroscopic and mechanical data are available. They are, however, limited in accuracy as a consequence of the approximations needed to carry out the calculations and the limited accuracy of the spectroscopic data. 

The fundamental vibrations have been assigned for the M-H-M backbone of HM COho, M = Cr, Mo, and W. When it is observable, the asymmetric M-H-M stretch occurs around 1700 cm-1 in low temperature ir spectra. One or possibly two deformation modes occur around 850 cm l in conjunction with overtones that are enhanced in intensity by Fermi resonance. The symmetric stretch, which involves predominantly metal motion, is expected below 150 cm l. For the molybdenum and tungsten compounds, this band is obscured by other low frequency features. Vibrational spectroscopic evidence is presented for a bent Cr-H-Cr array in [PPN][(OC)5Cr-H-Cr(CO)5], This structural inference is a good example of the way in which vibrational data can supplement diffraction data in the structural analysis of disordered systems. Implications of the bent Cr-H-Cr array are discussed in terms of a simple bonding model which involves a balance between nuclear repulsion, M-M overlap, and M-H overlap. The literature on M-H -M frequencies is summarized. 

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